Birth and death are the most relevant processes in determining
the dynamics of biological populations which in the context of
statistical physics can be modeled using interacting particle
models where particle number is changing in time. As it is
understood by now, birth and death processes are also
responsible for clustering mechanisms in systems where
random-walking individuals undergo reproduction and death. As a
result, aggregation of organisms can occur even in simple
models where birth and death processes are combined with
spatial diffusion. In fact, in the most simple Brownian
bug model, where particles reproduce and die with the same
probability and undergo Brownian motion
[1]}, [2]}, [3]}, clustering of
particles was observed. In this model the clustering is
produced simply by the reproductive correlations (the offspring
is born at the same location of the parent) and by the
irreversibility of the death process. Birth and death models of
moving individuals are the pertinent framework to capture
properties of biological systems such as planktonic populations
[2]}, or patterns in amoebae
[5]} and bacteria [6]}.
